Exponential Synchronization of Memristive HIndmarsh-Rose Neural Networks

TL;DR

This paper introduces a memristive Hindmarsh-Rose neural network model and rigorously proves exponential synchronization under certain coupling conditions, advancing understanding of neural network dynamics.

Contribution

It presents a novel memristive neural network model with proven exponential synchronization, highlighting the role of coupling strength thresholds.

Findings

Exponential synchronization occurs under specific coupling thresholds.

The model exhibits globally dissipative dynamics with absorbing sets.

Synchronization convergence rate is quantitatively established.

Abstract

A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and by leverage of integral inequalities tackling the linear network coupling against the memristive nonlineariry, it is rigorously proved that exponential synchronization at a uniform convergence rate occurs when the coupling strengths satisfy the threshold conditions quantitatively expressed by the parameters.